Solve for $c$. $\dfrac83c-2=\dfrac23 c-12$ $c=$
Explanation: We need to manipulate the equation to get $ c $ by itself. $\begin{aligned} \dfrac83c-2&=\dfrac23c-12 \\\\ \dfrac83c-2 {-\dfrac23c} &= \dfrac23c-12{-\dfrac23c} &&\gray{\text{Subtract } \dfrac23c \text{ from each side.}}\\\\ 2c-2&=-12 &&\gray{\text{Combine like terms.}}\\\\ 2c-2{+2} &= -12{+2} &&\gray{\text{Add 2 to each side.}}\\\\ 2c &=-10 &&\gray{\text{Combine like terms.}}\\\\ \dfrac{2c}{{2}} &= \dfrac{-10}{{2}} &&\gray{\text{Divide each side by 2.}}\\\\ c &= {-5} &&\gray{\text{Simplify.}}\\\\ \end{aligned}$ The answer: $c = { -5 }~~~~~~~~$ [Let's check our work!]